They answer that a keli rishon, which sat on the fire, retains the heat in its walls. A keli sheni may have contents that are just as hot, but because the walls of the keli aren't hot, the contents of the keli will cool too quickly to complete bishul.

Based on this Tosafot, the Hazon Ish rules that only liquids have a leniency of keli sheni, because they have contact with the walls of the container. A mass of solid food has a status of keli rishon even if you put it in a keli sheni, because it retains its heat better.

The posekim go on to consider which foods are so easily cooked that a keli sheni or even a keli shelishi can cook them. For example, the Mishnah Berurah and Arukh ha-Shulkhan both rule that a tea bag may not be placed even in a keli shelishi when the water is yad soledet bo, whereas the Igrot Moshe permits tea in a keli shelishi (Rabbi Simcha Bunim Cohen, The Shabbos Kitchen, Artscroll, page 32).

The Bavli's principle that keli sheni eino mevashel is thus more of an umdena than a principle. The keli sheni typically retains its heat for a more limited time, and the posekim must judge every food as to whether it will reach bishul in that time.

The Talmud Yerushalmi, however, has a different approach to keli rishon and sheni, which I found via this essay (.doc), which appears to be the work of Rav Shemuel Ariel, a ra"m in Otniel. In this approach, keli sheni is not based on the reality of heat, but the legal requirements of bishul.

The Yerushalmi quotes explanations from Rabbi Yosei and Rabbi Yonah in Shabbat 3:4:

Rabbi Yosei sounds similar to the Bavli: a keli sheni doesn't cook because it's not as hot. Rabbi Yonah, however, understands that even a keli rishon only has bishul by rabbinic decree, not mide-orayta.

According to Rabbi Ze'ira, bishul is “clearly” only when you have a fire going under the food. A keli rishon off the fire is exempt from bishul mide-orayta, and a keli sheni is exempt even mide-rabbanan. This is explicitly against the Bavli, which states on 39a that toledot ha-or are bishul mide-orayta.

The key issue in the Yerushalmi, then, isn't the reality of how hot the keli is, but its degree of removal from the fire. This fits particularly well with the language of rishon and sheni.

There is also somewhat of a middle approach between the Bavli and Yerushalmi. The Otsar Iyyunim in Mesivta cites an opinion held by the Or Sameah (Shabbat 9:2) and Hazon Ish (Yoreh De'ah 9:105) that applies the principle of removal from fire to the Bavli's understanding of keli sheni.

He writes that a keli sheni, even if capable of fully cooking a food, still only has the status of toladat toladat esh. It is too far removed from the fire to meet the Torah definition of bishul.

To summarize, we find two main approaches to understanding the leniency of keli sheni. The first, followed by the Bavli, rishonim, and posekim, is that the cooking ability of a keli sheni is generally inferior to that of a keli rishon. The second approach, which appears favored by the Yerushalmi, is that the keli sheni has too many degrees of removal from the fire to qualify for bishul, regardless of its cooking ability.